How do I twist this shape in a way that is 3D printable?
Making this structure into a manifold mesh could be tricky. Thankfully, 3-D printers do not care if meshes are technically separate if the faces are in the same mathematical position. If you can create one ring, you can duplicate it, and then move it up so the bottom of the new ring is exactly on the top of the lower one, or even intersecting it, and the 3-D printer will print one solid instead of something that breaks apart.